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Cálculo de Precipitaciones Máximas Mediante los Métodos Estadíst (Uso de los Factores de Frecuencia) Información de Precipitaciones Máximas para 38 años de registro Estación La Año PP PP Posición P >= PP (%) T (años) Y=Log PP mm mm m m/(N+1) (N+1)/m 1 2 3 4 5 6 7 1963 37.7 53.5 1 0.03 39.00 1.7284 1964 40.3 49.5 2 0.05 19.50 1.6946 1965 39.6 45.3 3 0.08 13.00 1.6561 1966 37.0 45.3 4 0.10 9.75 1.6561 1967 30.3 44.6 5 0.13 7.80 1.6493 1968 27.2 44.1 6 0.15 6.50 1.6444 1969 21.6 42.2 7 0.18 5.57 1.6253 1970 28.4 41.8 8 0.21 4.88 1.6212 1971 31.8 40.3 9 0.23 4.33 1.6053 1972 27.6 40.3 10 0.26 3.90 1.6053 1973 25.2 39.9 11 0.28 3.55 1.6010 1974 45.3 39.6 12 0.31 3.25 1.5977 1975 30.0 38.7 13 0.33 3.00 1.5877 1976 40.3 37.7 14 0.36 2.79 1.5763 1977 25.9 37.7 15 0.38 2.60 1.5763 1978 30.3 37 16 0.41 2.44 1.5682 1979 45.3 35.6 17 0.44 2.29 1.5514 1980 24.4 33.8 18 0.46 2.17 1.5289 1981 29.8 31.8 19 0.49 2.05 1.5024 1982 23.7 30.4 20 0.51 1.95 1.4829 1983 30.4 30.3 21 0.54 1.86 1.4814 1984 37.7 30.3 22 0.56 1.77 1.4814 1985 44.6 30 23 0.59 1.70 1.4771 1986 42.2 29.8 24 0.62 1.63 1.4742 1987 29.3 29.3 25 0.64 1.56 1.4669 1988 24.3 28.4 26 0.67 1.50 1.4533 1989 53.5 27.6 27 0.69 1.44 1.4409 1990 26.4 27.2 28 0.72 1.39 1.4346 1991 24.8 26.4 29 0.74 1.34 1.4216 1992 24.5 25.9 30 0.77 1.30 1.4133 1993 39.9 25.2 31 0.79 1.26 1.4014 1994 44.1 24.8 32 0.82 1.22 1.3945 1995 38.7 24.5 33 0.85 1.18 1.3892 1996 41.8 24.4 34 0.87 1.15 1.3874 1997 49.5 24.3 35 0.90 1.11 1.3856 1998 33.8 24.2 36 0.92 1.08 1.3838 1999 24.2 23.7 37 0.95 1.05 1.3747 2000 35.6 21.6 38 0.97 1.03 1.3345 Media 33.87 Media 1.5172 Desv. Est. 8.32 Des. Est. 0.1056 Cof. Asim. 0.4567 Cof. Asim. 0.1328 Análisis de Precipitaciones Máximas - Método Log-Normal T P K = Z Y PP (mm) años estimado antilog(Y)

Ejemplo Maximas Avenidas

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Page 1: Ejemplo Maximas Avenidas

Cálculo de Precipitaciones Máximas Mediante los Métodos Estadísticos(Uso de los Factores de Frecuencia)

Información de Precipitaciones Máximas para 38 años de registro Estación Laraqueri-Puno

Año PP PP Posición P >= PP (%) T (años) Y=Log PPmm mm m m/(N+1) (N+1)/m

1 2 3 4 5 6 7

1963 37.7 53.5 1 0.03 39.00 1.7284

1964 40.3 49.5 2 0.05 19.50 1.6946

1965 39.6 45.3 3 0.08 13.00 1.6561

1966 37.0 45.3 4 0.10 9.75 1.6561

1967 30.3 44.6 5 0.13 7.80 1.6493

1968 27.2 44.1 6 0.15 6.50 1.6444

1969 21.6 42.2 7 0.18 5.57 1.6253

1970 28.4 41.8 8 0.21 4.88 1.6212

1971 31.8 40.3 9 0.23 4.33 1.6053

1972 27.6 40.3 10 0.26 3.90 1.6053

1973 25.2 39.9 11 0.28 3.55 1.6010

1974 45.3 39.6 12 0.31 3.25 1.5977

1975 30.0 38.7 13 0.33 3.00 1.5877

1976 40.3 37.7 14 0.36 2.79 1.5763

1977 25.9 37.7 15 0.38 2.60 1.5763

1978 30.3 37 16 0.41 2.44 1.5682

1979 45.3 35.6 17 0.44 2.29 1.5514

1980 24.4 33.8 18 0.46 2.17 1.5289

1981 29.8 31.8 19 0.49 2.05 1.5024

1982 23.7 30.4 20 0.51 1.95 1.4829

1983 30.4 30.3 21 0.54 1.86 1.4814

1984 37.7 30.3 22 0.56 1.77 1.4814

1985 44.6 30 23 0.59 1.70 1.4771

1986 42.2 29.8 24 0.62 1.63 1.4742

1987 29.3 29.3 25 0.64 1.56 1.4669

1988 24.3 28.4 26 0.67 1.50 1.4533

1989 53.5 27.6 27 0.69 1.44 1.4409

1990 26.4 27.2 28 0.72 1.39 1.4346

1991 24.8 26.4 29 0.74 1.34 1.4216

1992 24.5 25.9 30 0.77 1.30 1.4133

1993 39.9 25.2 31 0.79 1.26 1.4014

1994 44.1 24.8 32 0.82 1.22 1.3945

1995 38.7 24.5 33 0.85 1.18 1.3892

1996 41.8 24.4 34 0.87 1.15 1.3874

1997 49.5 24.3 35 0.90 1.11 1.3856

1998 33.8 24.2 36 0.92 1.08 1.3838

1999 24.2 23.7 37 0.95 1.05 1.3747

2000 35.6 21.6 38 0.97 1.03 1.3345

Media 33.87 Media 1.5172

Desv. Est. 8.32 Des. Est. 0.1056

Cof. Asim. 0.4567 Cof. Asim. 0.1328

Análisis de Precipitaciones Máximas - Método Log-Normal

T P K = Z Y PP (mm)años estimado antilog(Y)

Page 2: Ejemplo Maximas Avenidas

2 0.50000 0.0000 1.5172 32.90

5 0.20000 0.8415 1.6061 40.37

10 0.10000 1.2817 1.6526 44.94

25 0.04000 1.7511 1.7022 50.37

50 0.02000 2.0542 1.7342 54.23

75 0.01333 2.2168 1.7514 56.41

100 0.01000 2.3268 1.7630 57.94

150 0.00667 2.4752 1.7787 60.07

200 0.00500 2.5762 1.7894 61.57

300 0.00333 2.7134 1.8038 63.66

400 0.00250 2.8074 1.8138 65.13

500 0.00200 2.8785 1.8213 66.26

1000 0.00100 3.0905 1.8437 69.77

Page 3: Ejemplo Maximas Avenidas

Análisis de Precipitaciones Máximas - Método de Gumbel

T P K PP (mm)años

2 0.50000 -0.1643 32.50

5 0.20000 0.7195 39.85

10 0.10000 1.3046 44.72

25 0.04000 2.0438 50.87

50 0.02000 2.5923 55.44

75 0.01333 2.9111 58.09

100 0.01000 3.1367 59.97

150 0.00667 3.4541 62.61

200 0.00500 3.6791 64.48

300 0.00333 3.9959 67.12

400 0.00250 4.2205 68.99

500 0.00200 4.3947 70.43

1000 0.00100 4.9355 74.93

Análisis de Precipitaciones Máximas - Método Log-Pearson Tipo III

T P K Y PP (mm)años estimado antilog(Y)

2 0.50000 -0.0221 1.5149 32.73

5 0.20000 0.8343 1.6054 40.30

10 0.10000 1.2950 1.6540 45.08

25 0.04000 1.7959 1.7069 50.93

50 0.02000 2.1248 1.7417 55.17

75 0.01333 2.3030 1.7605 57.61

100 0.01000 2.4242 1.7733 59.33

150 0.00667 2.5886 1.7907 61.75

200 0.00500 2.7012 1.8026 63.47

300 0.00333 2.8548 1.8188 65.88

400 0.00250 2.9605 1.8299 67.60

500 0.00200 3.0407 1.8384 68.93

1000 0.00100 3.2815 1.8638 73.09

Comparación de los Valores de Precipitaciones Máximas Obtenidos

T P PP (mm) PP (mm) PP (mm)años Log-Normal Gumbel Log-Pearson

2 0.50000 32.90 32.50 32.73

Page 4: Ejemplo Maximas Avenidas

5 0.20000 40.37 39.85 40.30

10 0.10000 44.94 44.72 45.08

25 0.04000 50.37 50.87 50.93

50 0.02000 54.23 55.44 55.17

75 0.01333 56.41 58.09 57.61

100 0.01000 57.94 59.97 59.33

150 0.00667 60.07 62.61 61.75

200 0.00500 61.57 64.48 63.47

300 0.00333 63.66 67.12 65.88

400 0.00250 65.13 68.99 67.60

500 0.00200 66.26 70.43 68.93

1000 0.00100 69.77 74.93 73.09

Page 5: Ejemplo Maximas Avenidas

Cálculo de los Límites de Confianza - Método Log-NormalGrados de libertad: 28 - 2 = 26 t (estad.) = 2.056

T P K = Z Y IC(Y) LCI(Y) LCS(Y) LCI(PP) LCS(PP)años

2 0.50000 0.0000 1.5172 0.0410 1.4762 1.5583 29.94 36.16

5 0.20000 0.8415 1.6061 0.0478 1.5584 1.6539 36.17 45.07

10 0.10000 1.2817 1.6526 0.0554 1.5972 1.7080 39.56 51.05

25 0.04000 1.7511 1.7022 0.0653 1.6369 1.7675 43.34 58.55

50 0.02000 2.0542 1.7342 0.0724 1.6618 1.8066 45.90 64.06

75 0.01333 2.2168 1.7514 0.0763 1.6751 1.8277 47.32 67.25

100 0.01000 2.3268 1.7630 0.0790 1.6840 1.8420 48.30 69.51

150 0.00667 2.4752 1.7787 0.0827 1.6959 1.8614 49.65 72.68

200 0.00500 2.5762 1.7894 0.0853 1.7041 1.8746 50.59 74.93

300 0.00333 2.7134 1.8038 0.0888 1.7150 1.8926 51.89 78.10

400 0.00250 2.8074 1.8138 0.0912 1.7225 1.9050 52.79 80.35

500 0.00200 2.8785 1.8213 0.0931 1.7282 1.9144 53.48 82.10

1000 0.00100 3.0905 1.8437 0.0986 1.7450 1.9423 55.60 87.56

Cálculo de los Límites de Confianza - Método de GumbelGrados de libertad: 28 - 2 = 26 t (estad.) = 2.056

T P K PP (mm) IC(PP) LCI(PP) LCS(PP)años

2 0.50000 -0.1643 32.50 3.25 29.25 35.76

5 0.20000 0.7195 39.85 3.63 36.23 43.48

10 0.10000 1.3046 44.72 4.40 40.32 49.12

25 0.04000 2.0438 50.87 5.68 45.19 56.56

50 0.02000 2.5923 55.44 6.75 48.69 62.19

75 0.01333 2.9111 58.09 7.40 50.69 65.49

100 0.01000 3.1367 59.97 7.87 52.10 67.83

150 0.00667 3.4541 62.61 8.53 54.08 71.14

200 0.00500 3.6791 64.48 9.01 55.47 73.49

300 0.00333 3.9959 67.12 9.69 57.43 76.81

400 0.00250 4.2205 68.99 10.18 58.81 79.16

500 0.00200 4.3947 70.43 10.55 59.88 80.99

1000 0.00100 4.9355 74.93 11.74 63.20 86.67

Cálculo de los Límites de Confianza - Método Log-Pearson Tipo IIIGrados de libertad: 28 - 3 = 25 t (estad.) = 2.06

T P K Y IC(Y) LCI(Y) LCS(Y) LCI(PP) LCS(PP)años

2 0.50000 -0.0221 1.5149 0.0411 1.4738 1.5560 29.77 35.98

Page 6: Ejemplo Maximas Avenidas

5 0.20000 0.8343 1.6054 0.0477 1.5576 1.6531 36.11 44.99

10 0.10000 1.2950 1.6540 0.0558 1.5983 1.7098 39.65 51.26

25 0.04000 1.7959 1.7069 0.0665 1.6405 1.7734 43.70 59.35

50 0.02000 2.1248 1.7417 0.0742 1.6675 1.8159 46.50 65.45

75 0.01333 2.3030 1.7605 0.0786 1.6819 1.8391 48.07 69.04

100 0.01000 2.4242 1.7733 0.0816 1.6917 1.8549 49.17 71.60

150 0.00667 2.5886 1.7907 0.0858 1.7049 1.8764 50.69 75.24

200 0.00500 2.7012 1.8026 0.0887 1.7139 1.8912 51.75 77.84

300 0.00333 2.8548 1.8188 0.0926 1.7261 1.9114 53.23 81.55

400 0.00250 2.9605 1.8299 0.0954 1.7345 1.9253 54.27 84.20

500 0.00200 3.0407 1.8384 0.0975 1.7409 1.9359 55.07 86.28

1000 0.00100 3.2815 1.8638 0.1039 1.7599 1.9677 57.54 92.84

Page 7: Ejemplo Maximas Avenidas

FACTOR DE FRECUENCIA K = Z FACTOR DE FRECUENCIA KDISTRIBUCION NORMAL DISTRIBUCION TIPO I - GUMBEL

Coeficiente

T P W K T P Kaños años

1 1.00000 infinito infinito 1 1.00000 infinito

2 0.50000 1.1774 0.0000 2 0.50000 -0.1643

3 0.33333 1.4823 0.4303 3 0.33333 0.2538

4 0.25000 1.6651 0.6742 4 0.25000 0.5214

5 0.20000 1.7941 0.8415 5 0.20000 0.7195

6 0.16667 1.8930 0.9674 6 0.16667 0.8770

8 0.12500 2.0393 1.1504 8 0.12500 1.1198

10 0.10000 2.1460 1.2817 10 0.10000 1.3046

15 0.06667 2.3273 1.5014 15 0.06667 1.6347

20 0.05000 2.4477 1.6452 20 0.05000 1.8658

25 0.04000 2.5373 1.7511 25 0.04000 2.0438

30 0.03333 2.6081 1.8343 30 0.03333 2.1887

35 0.02857 2.6666 1.9026 35 0.02857 2.3108

40 0.02500 2.7162 1.9604 40 0.02500 2.4163

45 0.02222 2.7592 2.0103 45 0.02222 2.5093

50 0.02000 2.7971 2.0542 50 0.02000 2.5923

55 0.01818 2.8310 2.0933 55 0.01818 2.6673

60 0.01667 2.8616 2.1285 60 0.01667 2.7358

65 0.01538 2.8894 2.1605 65 0.01538 2.7987

70 0.01429 2.9150 2.1898 70 0.01429 2.8569

75 0.01333 2.9385 2.2168 75 0.01333 2.9111

80 0.01250 2.9604 2.2418 80 0.01250 2.9617

85 0.01176 2.9808 2.2652 85 0.01176 3.0093

90 0.01111 2.9999 2.2870 90 0.01111 3.0541

95 0.01053 3.0179 2.3075 95 0.01053 3.0965

100 0.01000 3.0349 2.3268 100 0.01000 3.1367

125 0.00800 3.1075 2.4093 125 0.00800 3.3115

150 0.00667 3.1656 2.4752 150 0.00667 3.4541

175 0.00571 3.2140 2.5297 175 0.00571 3.5747

200 0.00500 3.2552 2.5762 200 0.00500 3.6791

250 0.00400 3.3231 2.6525 250 0.00400 3.8535

300 0.00333 3.3775 2.7134 300 0.00333 3.9959

350 0.00286 3.4228 2.7641 350 0.00286 4.1163

400 0.00250 3.4616 2.8074 400 0.00250 4.2205

450 0.00222 3.4955 2.8451 450 0.00222 4.3125

500 0.00200 3.5255 2.8785 500 0.00200 4.3947

550 0.00182 3.5524 2.9084 550 0.00182 4.4691

600 0.00167 3.5769 2.9355 600 0.00167 4.5370

650 0.00154 3.5992 2.9603 650 0.00154 4.5994

700 0.00143 3.6197 2.9830 700 0.00143 4.6573

750 0.00133 3.6387 3.0041 750 0.00133 4.7111

800 0.00125 3.6564 3.0236 800 0.00125 4.7614

850 0.00118 3.6729 3.0419 850 0.00118 4.8087

900 0.00111 3.6885 3.0591 900 0.00111 4.8533

950 0.00105 3.7031 3.0753 950 0.00105 4.8955

1000 0.00100 3.7169 3.0905 1000 0.00100 4.9355

1500 0.00067 3.8245 3.2090 1500 0.00067 5.2518

2000 0.00050 3.8989 3.2908 2000 0.00050 5.4762

2500 0.00040 3.9558 3.3530 2500 0.00040 5.6502

3000 0.00033 4.0016 3.4031 3000 0.00033 5.7924

3500 0.00029 4.0399 3.4450 3500 0.00029 5.9126

4000 0.00025 4.0728 3.4809 4000 0.00025 6.0167

4500 0.00022 4.1017 3.5124 4500 0.00022 6.1086

5000 0.00020 4.1273 3.5402 5000 0.00020 6.1907

7500 0.00013 4.2244 3.6458 7500 0.00013 6.5069

8000 0.00013 4.2396 3.6624 8000 0.00013 6.5572

10000 0.00010 4.2919 3.7191 10000 0.00010 6.7312

Page 8: Ejemplo Maximas Avenidas

FACTOR DE FRECUENCIA K PARA LA DISTRIBUCION DE PEARSON - TIPO III

Coeficiente PERIODO DE RETORNO (AÑOS)

de 2 5 10 25 50 75 100 200 500 1000

Asimetría PPROBABILIDAD DE EXCEDENCIA

(c) 0.500 0.200 0.100 0.040 0.020 0.013 0.010 0.005 0.002 0.001

-2.6 0.3469 0.6901 0.7460 0.7589 0.7594 0.7616 0.7648 0.7807 0.8224 0.8716

-2.5 0.3401 0.7055 0.7716 0.7909 0.7916 0.7924 0.7940 0.8037 0.8331 0.8702

-2.4 0.3326 0.7202 0.7973 0.8242 0.8265 0.8266 0.8271 0.8323 0.8517 0.8783

-2.3 0.3242 0.7342 0.8229 0.8588 0.8638 0.8640 0.8641 0.8662 0.8777 0.8958

-2.2 0.3152 0.7476 0.8484 0.8945 0.9034 0.9045 0.9047 0.9051 0.9109 0.9221

-2.1 0.3054 0.7602 0.8737 0.9312 0.9451 0.9479 0.9486 0.9489 0.9510 0.9570

-2.0 0.2949 0.7721 0.8989 0.9688 0.9887 0.9939 0.9958 0.9972 0.9976 1.0001

-1.9 0.2839 0.7832 0.9237 1.0072 1.0342 1.0424 1.0460 1.0499 1.0505 1.0510

-1.8 0.2722 0.7936 0.9483 1.0462 1.0813 1.0932 1.0989 1.1066 1.1094 1.1095

-1.7 0.2600 0.8032 0.9724 1.0858 1.1299 1.1461 1.1545 1.1672 1.1739 1.1752

-1.6 0.2473 0.8120 0.9962 1.1259 1.1799 1.2009 1.2124 1.2314 1.2439 1.2477

-1.5 0.2340 0.8201 1.0194 1.1663 1.2311 1.2576 1.2726 1.2990 1.3189 1.3267

-1.4 0.2204 0.8273 1.0421 1.2069 1.2833 1.3159 1.3349 1.3697 1.3988 1.4120

-1.3 0.2063 0.8338 1.0643 1.2477 1.3365 1.3756 1.3990 1.4434 1.4832 1.5031

-1.2 0.1919 0.8394 1.0858 1.2886 1.3904 1.4366 1.4647 1.5198 1.5719 1.5998

-1.1 0.1771 0.8442 1.1066 1.3293 1.4450 1.4988 1.5320 1.5987 1.6646 1.7019

-1.0 0.1620 0.8481 1.1268 1.3700 1.5002 1.5619 1.6007 1.6800 1.7610 1.8089

-0.9 0.1466 0.8513 1.1462 1.4104 1.5557 1.6259 1.6705 1.7633 1.8610 1.9205

-0.8 0.1309 0.8536 1.1648 1.4506 1.6115 1.6906 1.7414 1.8485 1.9642 2.0366

-0.7 0.1151 0.8550 1.1826 1.4903 1.6675 1.7558 1.8131 1.9355 2.0704 2.1568

-0.6 0.0990 0.8556 1.1996 1.5296 1.7235 1.8215 1.8855 2.0239 2.1794 2.2808

-0.5 0.0828 0.8553 1.2157 1.5683 1.7794 1.8874 1.9585 2.1137 2.2909 2.4084

-0.4 0.0664 0.8543 1.2308 1.6064 1.8351 1.9535 2.0319 2.2046 2.4047 2.5393

-0.3 0.0499 0.8523 1.2450 1.6438 1.8906 2.0196 2.1055 2.2965 2.5206 2.6732

-0.2 0.0333 0.8495 1.2583 1.6804 1.9456 2.0856 2.1793 2.3892 2.6384 2.8099

-0.1 0.0167 0.8459 1.2705 1.7162 2.0002 2.1514 2.2531 2.4825 2.7577 2.9491

0.0 0.0000 0.8415 1.2817 1.7511 2.0542 2.2168 2.3268 2.5762 2.8785 3.0905

0.1 -0.0167 0.8362 1.2919 1.7850 2.1075 2.2818 2.4002 2.6703 3.0005 3.2340

0.2 -0.0333 0.8301 1.3011 1.8180 2.1600 2.3462 2.4733 2.7645 3.1235 3.3793

0.3 -0.0499 0.8232 1.3091 1.8499 2.2117 2.4100 2.5458 2.8588 3.2474 3.5262

0.4 -0.0664 0.8155 1.3161 1.8806 2.2625 2.4731 2.6178 2.9528 3.3719 3.6744

0.5 -0.0828 0.8070 1.3221 1.9103 2.3123 2.5353 2.6890 3.0466 3.4968 3.8237

0.6 -0.0990 0.7978 1.3269 1.9387 2.3610 2.5965 2.7595 3.1400 3.6220 3.9740

0.7 -0.1151 0.7878 1.3306 1.9659 2.4085 2.6567 2.8290 3.2329 3.7473 4.1250

0.8 -0.1309 0.7771 1.3332 1.9918 2.4548 2.7159 2.8975 3.3250 3.8726 4.2765

0.9 -0.1466 0.7657 1.3348 2.0164 2.4999 2.7738 2.9650 3.4164 3.9976 4.4283

1.0 -0.1620 0.7536 1.3352 2.0397 2.5437 2.8305 3.0312 3.5069 4.1223 4.5802

1.1 -0.1771 0.7409 1.3346 2.0617 2.5860 2.8859 3.0962 3.5963 4.2464 4.7321

1.2 -0.1919 0.7275 1.3328 2.0822 2.6270 2.9399 3.1599 3.6846 4.3698 4.8838

1.3 -0.2063 0.7135 1.3301 2.1014 2.6665 2.9925 3.2222 3.7718 4.4925 5.0350

1.4 -0.2204 0.6990 1.3262 2.1191 2.7045 3.0435 3.2830 3.8576 4.6141 5.1858

1.5 -0.2340 0.6839 1.3214 2.1355 2.7410 3.0930 3.3423 3.9420 4.7348 5.3358

1.6 -0.2473 0.6683 1.3155 2.1504 2.7759 3.1410 3.4000 4.0249 4.8542 5.4850

1.7 -0.2600 0.6523 1.3087 2.1639 2.8092 3.1873 3.4561 4.1063 4.9723 5.6331

1.8 -0.2722 0.6358 1.3009 2.1760 2.8409 3.2319 3.5105 4.1860 5.0890 5.7801

1.9 -0.2839 0.6190 1.2922 2.1867 2.8710 3.2749 3.5632 4.2641 5.2043 5.9259

2.0 -0.2949 0.6018 1.2826 2.1960 2.8995 3.3162 3.6142 4.3404 5.3179 6.0703

2.1 -0.3054 0.5843 1.2721 2.2039 2.9263 3.3557 3.6634 4.4149 5.4298 6.2131

2.2 -0.3152 0.5667 1.2608 2.2105 2.9515 3.3935 3.7108 4.4876 5.5399 6.3544

2.3 -0.3242 0.5488 1.2488 2.2157 2.9750 3.4295 3.7564 4.5583 5.6482 6.4939

2.4 -0.3326 0.5308 1.2361 2.2196 2.9970 3.4638 3.8001 4.6272 5.7546 6.6317

2.5 -0.3401 0.5128 1.2227 2.2222 3.0173 3.4963 3.8420 4.6940 5.8589 6.7675

2.6 -0.3469 0.4947 1.2087 2.2236 3.0360 3.5271 3.8821 4.7589 5.9613 6.9013

2.7 -0.3527 0.4768 1.1942 2.2238 3.0532 3.5561 3.9204 4.8218 6.0615 7.0331

2.8 -0.3577 0.4589 1.1791 2.2228 3.0688 3.5834 3.9568 4.8826 6.1596 7.1628

2.9 -0.3616 0.4413 1.1637 2.2208 3.0829 3.6091 3.9914 4.9415 6.2556 7.2902

Page 9: Ejemplo Maximas Avenidas

t t/Tp q q/qp0.00 0.00 0.00 0.00

2.00 0.10 3.00 0.03

6.00 0.30 19.00 0.19

8.00 0.40 31.00 0.31

12.00 0.60 66.00 0.66

14.00 0.70 82.00 0.82

16.00 0.80 93.00 0.93

18.00 0.90 99.00 0.99

20.00 1.00 100.00 1.00

22.00 1.10 99.00 0.99

24.00 1.20 93.00 0.93

26.00 1.30 86.00 0.86

30.00 1.50 68.00 0.68

34.00 1.70 46.00 0.46

38.00 1.90 33.00 0.33

44.00 2.20 21.00 0.21

52.00 2.60 11.00 0.11

64.00 3.20 4.00 0.04

100.00 5.00 0.00 0.00

Tp = 0.833 qp = 7.49

t q0.00 0.00 0.00 0.00

0.10 0.08 0.03 0.22

0.30 0.25 0.19 1.42

0.40 0.33 0.31 2.32

0.60 0.50 0.66 4.94

0.70 0.58 0.82 6.14

0.80 0.67 0.93 6.97

0.90 0.75 0.99 7.42

1.00 0.83 1.00 7.49

1.10 0.92 0.99 7.42

1.20 1.00 0.93 6.97

1.30 1.08 0.86 6.44

1.50 1.25 0.68 5.09

1.70 1.42 0.46 3.45

1.90 1.58 0.33 2.47

2.20 1.83 0.21 1.57

2.60 2.17 0.11 0.82

3.20 2.67 0.04 0.30

5.00 4.17 0.00 0.00

t/Tp q/qp

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Hidrograma unitario adimensional SCS

t/Tp

q/q

p

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Hidrograma Generado

t (horas)

q (

m3

/s.c

m)

Page 10: Ejemplo Maximas Avenidas

Método de GumbelT (años) PP (mm) LCI(PP) LCS(PP)

2 32.50 29.25 35.765 39.85 36.23 43.48

10 44.72 40.32 49.1225 50.87 45.19 56.5650 55.44 48.69 62.1975 58.09 50.69 65.49

100 59.97 52.10 67.83150 62.61 54.08 71.14200 64.48 55.47 73.49300 67.12 57.43 76.81400 68.99 58.81 79.16500 70.43 59.88 80.99

1000 74.93 63.20 86.67

Page 11: Ejemplo Maximas Avenidas

T Log-Normal Gumbel Log-Pearson2 32.90 32.50 32.735 40.37 39.85 40.30

10 44.94 44.72 45.0825 50.37 50.87 50.9350 54.23 55.44 55.1775 56.41 58.09 57.61

100 57.94 59.97 59.33150 60.07 62.61 61.75200 61.57 64.48 63.47300 63.66 67.12 65.88400 65.13 68.99 67.60500 66.26 70.43 68.93

1000 69.77 74.93 73.09

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

COMPARATIVO DE MÉTODOS DE DISTRIBUCIÓN DE PROBABILIDAD ESTACIÓN LARAQUERI

Log-Normal Gumbel Log-PearsonTiempo de retorno (años)

Pre

cip

itació

n M

áxim

a (

mm

)

Page 12: Ejemplo Maximas Avenidas

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

COMPARATIVO DE MÉTODOS DE DISTRIBUCIÓN DE PROBABILIDAD ESTACIÓN LARAQUERI

Log-Normal Gumbel Log-PearsonTiempo de retorno (años)

Pre

cip

itació

n M

áxim

a (

mm

)